i was trying to get a particular solution of a 3rd order ODE using the variation of parameters method(adsbygoogle = window.adsbygoogle || []).push({});

the homogeneous solution is y_{h}= c_{1 }e^{-x}+ c_{2 }e^{x}+ c_{3}e^{2x}

the particular solution is y_{p}=y_{1}u_{1}+y_{2}u_{2}+y_{3}u_{3}

as u_{1}=∫ (w_{1}g(x) /w) dx , u_{2}=∫ (w_{2}g(x) /w) dx , u_{3}=∫ (w_{3}g(x) /w) dx

w =

|y_{1}y_{2}y_{3}|

|y'_{1}y'_{2}y'_{3}|

|y''_{1}y''_{2}y''_{3}|

when i choose y_{1}, y_{2}, y_{3}to be e^{-x},e^{x},e^{2x}i get an answer ,

but when i change the arrangement (like: e^{x},e^{-x},e^{2x})

i get another different answer !

so , i have two questions

1 is it normal to have different results when changing who is y_{1}, y_{2}, y_{3}, or am i doing something wrong?

2 if it is normal , does that mean i can have too many different particular solutions , just by changing who is y_{1}, y_{2}, y_{3}?

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# Variation of parameters - i have different particular soluti

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